Question
In: Finance
Lionel deposited $1,500 at the end of every month into an RRSP for 6 years. The...
Lionel deposited $1,500 at the end of every month into an RRSP for 6 years. The interest rate earned was 3.75% compounded semi-annually for the first 3 years and changed to 4.00% compounded monthly for the next 3 years. What was the accumulated value of the RRSP at the end of 6 years?
Round to the nearest cent
Solutions
Expert Solution
As we Know for first three years it is compunded semi annually, so in the given table i have taken months, amount deposited monthly, total and Interest.
Where Interest for first 6 months(if for semi annually compunded ) = A*3.75%*6/12 = 168.74$
For next semi annual compounding interest = Total * Interest rate * Period of compounding/Number of months in an year
Total in first case = Total amount deposited till 6 months + Interest
Total from next 6 months = Total + Total Amount deposited for 6 months
| Month | Amount Deposited | Total | Interest |
| 1 | 1500 | ||
| 2 | 1500 | ||
| 3 | 1500 | ||
| 4 | 1500 | ||
| 5 | 1500 | ||
| 6 | 1500 | ||
| Toatl Amount | 9000 (A) | 9168.75 | 168.75 |
| 7 | 1500 | ||
| 8 | 1500 | ||
| 9 | 1500 | ||
| 10 | 1500 | ||
| 11 | 1500 | ||
| 12 | 1500 | ||
| Toatl Amount | 9000 | 18168.75 | 340.6640625 |
| 13 | 1500 | ||
| 14 | 1500 | ||
| 15 | 1500 | ||
| 16 | 1500 | ||
| 17 | 1500 | ||
| 18 | 1500 | ||
| Toatl Amount | 9000 | 27168.75 | 509.4140625 |
| 19 | 1500 | ||
| 20 | 1500 | ||
| 21 | 1500 | ||
| 22 | 1500 | ||
| 23 | 1500 | ||
| 24 | 1500 | ||
| Toatl Amount | 9000 | 36168.75 | 678.1640625 |
| 25 | 1500 | ||
| 26 | 1500 | ||
| 27 | 1500 | ||
| 28 | 1500 | ||
| 29 | 1500 | ||
| 30 | 1500 | ||
| Toatl Amount | 9000 | 45168.75 | 846.9140625 |
| 31 | 1500 | ||
| 32 | 1500 | ||
| 33 | 1500 | ||
| 34 | 1500 | ||
| 35 | 1500 | ||
| 36 | 1500 | ||
| Toatl Amount | 9000 | 54168.75 | 1015.664063 |
| 37 | 1500 | 55668.75 | 185.5625 |
| 38 | 1500 | 57168.75 | 190.5625 |
| 39 | 1500 | 58668.75 | 195.5625 |
| 40 | 1500 | 60168.75 | 200.5625 |
| 41 | 1500 | 61668.75 | 205.5625 |
| 42 | 1500 | 63168.75 | 210.5625 |
| 43 | 1500 | 64668.75 | 215.5625 |
| 44 | 1500 | 66168.75 | 220.5625 |
| 45 | 1500 | 67668.75 | 225.5625 |
| 46 | 1500 | 69168.75 | 230.5625 |
| 47 | 1500 | 70668.75 | 235.5625 |
| 48 | 1500 | 72168.75 | 240.5625 |
| 49 | 1500 | 73668.75 | 245.5625 |
| 50 | 1500 | 75168.75 | 250.5625 |
| 51 | 1500 | 76668.75 | 255.5625 |
| 52 | 1500 | 78168.75 | 260.5625 |
| 53 | 1500 | 79668.75 | 265.5625 |
| 54 | 1500 | 81168.75 | 270.5625 |
| 55 | 1500 | 82668.75 | 275.5625 |
| 56 | 1500 | 84168.75 | 280.5625 |
| 57 | 1500 | 85668.75 | 285.5625 |
| 58 | 1500 | 87168.75 | 290.5625 |
| 59 | 1500 | 88668.75 | 295.5625 |
| 60 | 1500 | 90168.75 | 300.5625 |
| 61 | 1500 | 91668.75 | 305.5625 |
| 62 | 1500 | 93168.75 | 310.5625 |
| 63 | 1500 | 94668.75 | 315.5625 |
| 64 | 1500 | 96168.75 | 320.5625 |
| 65 | 1500 | 97668.75 | 325.5625 |
| 66 | 1500 | 99168.75 | 330.5625 |
| 67 | 1500 |
100668.75
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